Laser arrangement including a cavity defined by convex and concave mirrors

ABSTRACT

A laser cavity defined by convex and concave mirrors and including a discrete intracavity lens is characterized by a relatively large TEMoo spot radius, a short physical length and good stability.

I United States Patent A R 1151 3,680,000

BEST VAILABL 1 FY Chesler et al. [451 July 25, 1972 [54] LASER ARRANGEMENT INCLUDING A 3,487,331 12/1969 Gates ..331/94.s CAVITY DEFINED BY CONVEX AND 3,440,561 4/1969 Pole et al.... .....331/94.5 CONCAVE MIRR 3,513,402 5/1970 Marrison ..331/94.5 ORS 3,397,362 8/1968 Grayson et al.. .....331/94.5 [72] Inventors: Ronald Benjamin Cheller, Summit; Dan 3,435,363 3/1969 Patel ..331/94.5

Maydan, Berkeley Heights, both of NJ. I OTHER PUBLICATIONS [73] Ass1gnee: Bell Telephone Laboratories, Incorporated,

Murray Hill, St1ckley, Laser Bnghtness Gain and Mode Control by Compensation for Thermal Distortion, IEEE J. Quant. Elect. Vol. [22] Flled: March 19, 1971 52 No, 4 pg I 21 A l.N 126,1 1 pp 0 33 Primary Examiner-William L. Siltes Attorney-R. J. Guenther and Kenneth B. Hamlin [52] U.S. Cl ..331/94.5 [51] Int. CL... ..l-l0ls 3/08 [57] ABSTRACT 5 8 F ld t h 1 0 Sean 331/94 356/106 350/202 A laser cavity defined by convex and concave mirrors and in- 56 eluding a discrete intracavity lens is characterized by a rela- 1 References Cited tively large TEM spot radius, a short physical length and I UNITED STATES PATENTS 89 stability- 3,434,073 3/1969 Furkner ..33 l/94.5 5 Chin, 4 Drawing figures PATENTEDJMB 1m 3.680.000

R. B. CHESLER uvvavroes D. MAYDAN BVIZW M an? A T TOP/V5 P LASER ARRANGEMENT INCLUDING A CAVITY DEFINED BY CONVEX AND CONCAVE MIRRORS BACKGROUND OF THE INVENTION Optimal operation of a solid-state laser in the transverse TEM,, mode requires that the optical spot radius (l/e intensity) within the active laser element be about one-half the radius of the laser element. If this condition is approximately satisfied, the TEM mode will oscillate with the minimum diffraction losses consistent with the suppression of higher-order transverse modes.

Several techniques are known for achieving a suitably large TEM, mode radius within the active element of a solid-state laser arrangement. One of these involves forming convex mirror surfaces on the respective ends of the element. The successful operation of such an arrangement depends on the existence of thermal focusing within the pumped element. This design has three drawbacks: l the arrangement has marginal stability (according to the stability criteria specified in the Kogelnik reference cited hereinbelow), and thermal and mechanical perturbations produce significant fluctuations in the power output thereof; (2) the thermal focusing action is imperfect; and (3) operation of the arrangement is restricted to a fixed input power.

Another known technique involves the use of a nearly concentric cavity that includes spaced-apart planar and concave mirrors. Typically, for a laser element about l0 cm in length, the distance between these mirrors approximates 70 cm. Arrangements of this type using shorter mirror radii and mirror separations are inefficient because of the significant variation of mode radius that then occurs from one end of the laser element to the other. In addition, such shorter arrangements operate near the boundary of instability.

SUMMARY OF THE INVENTION An object of the present invention is an improved laser arrangement.

More specifically, an object of this invention is a simple solid-state laser that is compact, stable and efficient.

Another object of the present invention is a laser arrangement that is particularly suitable for intracavity modulation and nonlinear conversion applications.

These and other objects of the present invention are realized in a specific illustrative embodiment thereof that comprises a laser arrangement featuring a convex minor, a lens having a focal length f, an active laser element positioned between the convex mirror and the lens and a concave mirror spaced a distance p from the lens to satisfy the relationship f BRIEF DESCRIPTION OF THE DRAWING A complete understanding of the present invention and of the above and other objects, features and advantages thereof may be gained from a consideration of the following detailed description of an illustrative embodiment thereof presented hereinbelow in connection with the accompanying drawing, in which:

FIGS. 1 and 2 each show a prior art laser arrangement;

FIG. 3 depicts a specific illustrative laser arrangement made in accordance with the principles of the present invention; and

FIG. 4 shows an equivalent representation of the FIG. 3 arrangement.

DETAILED DESCRIPTION One prior art technique for achieving a relatively large TEM mode radius within the active element of a solid-state laser arrangement is depicted in simplified form in FIG. 1. As shown, the respective ends and 12 of a solid-state laser element 15 are shaped to form convex mirror surfaces. When conventionally pumped by a suitable means (not shown), the depicted arrangement is effective to establish a relatively large TEM spot radius within the element 15. The profile of the TEM mode within the element 15 is represented approximately by dashed lines 16 and 18.

As indicated earlier above, the successful operation of a prior art arrangement of the type shown in FIG. 1 depends on the existence of thermal focusing (arising from a temperature gradient) within the pumped element 15. But, as stated before, such a focusing action is imperfect and, as a practical matter, attempts to constrain the focusing action within prescribed limits cause the operation of the arrangement to be limited to a fixed input power. Also, in actual operation, the illustrated arrangement possesses marginal stability. Moreover, thermal and mechanical perturbations affect the performance of the arrangement by producing significant fluctuations in the output power thereof.

Another prior art laser arrangement, shown in FIG. 2, comprises a nearly concentric cavity encompassed by a planar mirror surface 20 and a concave mirror surface 22. Such an arrangement is effective to define a TEM,, mode (represented by dashed lines 26 and 28) that expands to a relatively large size within laser element 25 near the mirror surface 22. Again, a thermal-focusing action is assumed to be present within the element 25, so that the effective radius of the surface 22 is only slightly greater than the separation between the surfaces 20 and 22.

The primary disadvantage of the FIG. 2 arrangement is its relatively long length. In one typical case, in which the length of the laser element 25 was only about 10 cm, the distance between the mirror surfaces 20 and 22 was required for efficient operation to be approximately cm.

Shorter cavities of the FIG. 2 type can be constructed but, as the mirrors of such a cavity are moved closer together and as the radius of curvature of the concave surface thereof is decreased, the arrangement becomes relatively inefficient. This is so because of the significant variation of mode radius that then occurs within the element 25 from one end to the other. Also, such shorter cavities operate near the boundary of instability.

FIG. 3 shows a specific illustrative laser arrangement that embodies the principles of the present invention. The depicted arrangement constitutes a compact structure for achieving a large TEM,, mode radius. The arrangement, which is characterized by good stability, comprises an active laser element 35 (for example, a rod of NdzYAlG) a conventional pump source 37, a convex mirror surface 30 having a radius of curvature R a positive lens 31 having a focal length f and a concave mirror surface 32, having a radius R,,, located a distance p from the lens 31. In accordance with the principles of this invention, the inequality f p must be satisfied.

For illustrative purposes the elements 30 and 31 are shown in FIG. 3 as being formed (for example, ground) on the respective ends of the rod 35. Although such an integral structure is generally advantageous, it is to be understood that physically separate elements can be combined with the rod 35 to achieve an equivalent configuration.

The profile of the TEM,, mode within the laser element 35 of FIG. 3 is represented by dashed lines 36 and 38. As shown in FIG. 3 the beam represented by the lines 36 and 38 includes a focused or small-waist portion between the lens 31 and the mirror surface 32. (The beam so indicated is intended to be representative of the arrangement operating in either a continuous or a pulsed mode.) Because it provides a focused beam, the depicted arrangement is well suited to be combined with a modulator element or a non-linear element (positioned, for example, at the location of a dashed-outline element 39) to form an intracavity modulator or converter unit. By way of example, an arrangement of the type shown in FIG. 3 facilitates acousto-optic cavity dumping and Q-switching, which are described by applicants in Cavity Dumping and Q-Switching of Nd:YAlG Lasers," Journal Applied Physics, Feb. 1970. In general, the focused beam provided by the FIG. 3 arrangement is advantageous for use in conjunction with electro-optic modulators and nonlinear optical devices such as parametric oscillators and harmonic generators.

There are an infinite number of sets of parameters which define the same mode radius within the laser rod 35 shown in FIG. 3. Shorter, more compact designs can be realized by selecting small values off and.R,. As a practical matter the limit of short cavity designs is determined by problems in fabricating high-quality mirrors having short radii of curvature. Another practical limit to achieving short cavity structures is provided by the increasingly smaller spot radius and therefore higher light intensity that is formed at the mirror surface 32. As the spot radius decreases, the possibility of causing heat damage. to the surface 32 increases.

In general, the radius R,. of the convex mirror surface 30 shown in FIG. 3 should be large compared to the length of the laser rod 35 but, preferably, should be small enough to dominate over any thermal focusing that exists in the rod 35.

I A practical advantage of the arrangement shown in FIG. 3 is that small adjustments of the mode radius within the laser rod 35 can be easily made, with fixed values of R, R, and f, by merely varying the distance p. The ability to make such adjustments in this way simplifies the design of the depicted arrangement and increases the flexibility of using the arrangement in various applications of practical interest.

One particular illustrative set of values appropriate to achieve efficient and stable TEM mode operation in the FIG. 3 arrangement for an NdzYAlG laser rod 2.5 mm in diameter and cm in optical length is as follows: R, 100 cm, f 10 cm, p l3.5 cm, and R, 2.5 cm. For this specific set of values, the overall length of the depicted cavity arrangement wasonly 19 cm. In actual operation, for a predetermined set of pumping conditions the spot radius-at the beam waist (the narrowest cross section) between the elements 3] and 32 of the illustrated arrangement was 64 microns and measurements indicated that the arrangement was then providing 0.6 watts of continuous-wave TEM mode output power at 0.14 percent total power efficiency. By contrast, a conventional cavity 35 cm in length and including two 3-meter concave mirrors yielded only 0.45 watts of output power under the same pumping conditions using an active NdzYAlG laser rod of similar quality with flat and parallel antirefiection-coated ends.

For purposes of analysis only, it is useful to recognize that the laser arrangement illustrated in FIG. 3 can be redrawn as shown in FIG. 4. The basis for redrawing FIG. 3 is that the mirror surface 32 thereof can be considered to be imaged by the lens 31 into a mirror surface 42 (FIG. 4) which is located a distance d from the mirror surface 40. This transformation is governed by the usual laws of geometrical optics, which determine the radius and position of the mirror surface 42. The sun faces 40 and 42 form a lensless cavity whose properties can be calculated in a straightforward way using known formulas. (See, for example, Modes in Optical Resonators" by H. Kogelnik, Lasers, Volume I, edited by A. Levine, M. Dekker,

numerous other arrangements maybe devised by those skilled in the art without departing from the spirit andscope of the in- I vention.

What is claimed is: 1. In combination, a laser cavity having a main longitudinal axis, said cavity being defined by spaced-apart convex and concave mirror surfaces positioned along said axis,

an active laser element positioned along said axis between 1 said surfaces,

and a lens having a focal length f positioned along said axis between said element and said concave surface at a distance p from said concave surface to satisfy the in equality f p.

2. A laser arrangement having a main longitudinal axis, said arrangement comprisin a convex mirror positioned along said axis,

a lens, having a focal length f, positioned along said axis,

an active laser element positioned along said axis between said mirror and said lens,

and a concave mirror positioned along said axis and spaced a distance p from said lens to satisfy the relationship f p.

3. An arrangement as in claim 2 wherein said convex mirror and said lens are formed integral with and on the respective ends of said laser element.

4. An arrangement as in claim 3 wherein said laser element is made of NdzYAlG.

5. An arrangement as in claim 4 further including means for pumping said laser element to cause said arrangement to operate in the TEM transverse mode. 

1. In combination, a laser cavity having a main longitudinal axis, said cavity being defined by spaced-apart convex and concave mirror surfaces positioned along said axis, an active laser element positioned along said axis between said surfaces, and a lens having a focal length f positioned along said axis between said element and said concave surface at a distance p from said concave surface to satisfy the inequality f > p.
 2. A laser arrangement having a main longitudinal axis, said arrangement comprising a convex mirror positioned along said axis, a lens, having a focal length f, positioned along said axis, an active laser element positioned along said axis between said mirror and said lens, and a concave mirror positioned along said axis and spaced a distance p from said lens to satisfy the relationship f < p.
 3. An arrangement as in claim 2 wherein said convex mirror and said lens are formed integral with and on the respective ends of said laser element.
 4. An arrangement as in claim 3 wherein said laser element is made of Nd:YAlG.
 5. An arrangement as in claim 4 further including means for pumping said laser element to cause said arrangement to operate in the TEMoo transverse mode. 